Explanation:
We can use the formula for the nth term of an arithmetic sequence:
tn = a + (n - 1)d
where tn is the nth term, a is the first term, n is the number of terms, and d is the common difference.
We are given two pieces of information about this sequence:
t6 = 24
t15 = 21
We can use these equations to solve for a and d.
For t6 = 24:
t6 = a + (6 - 1)d
24 = a + 5d
For t15 = 21:
t15 = a + (15 - 1)d
21 = a + 14d
Now we have two equations with two unknowns. We can solve for a and d by subtracting the first equation from the second:
21 - 24 = (a + 14d) - (a + 5d)
-3 = 9d
d = -1/3
We can substitute this value of d into one of the equations to solve for a:
24 = a + 5(-1/3)
24 = a - 5/3
a = 24 + 5/3
a = 77/3
Now we have the first term (a) and the common difference (d) of the sequence:
a = 77/3
d = -1/3
To find the third term (t3), we can use the formula:
t3 = a + (3 - 1)d
t3 = 77/3 + 2(-1/3)
t3 = 77/3 - 2/3
t3 = 75/3
t3 = 25
Therefore, the third term of the sequence is 25